An optimization method to design a skip–stop pattern for renovating operation schemes in urban railways

This study deals with an optimization problem to design an A/B skip–stop pattern (A/B SSP) to renovate operation schemes in urban railways. The A/B SSP is especially useful for urban railways since the renovation does not require a restructuring of infrastructure. The renovation improves passengers’ travel time along with lost passengers owing to selective stops. This study aims to achieve two goals that are minimizing the lost passengers and the travel time during the renovation. To this end, we first present a mathematical model based on a network flow model. The model explicitly maximizes transportation volume and implicitly controls the travel time by the number of stop stations under operational constraints. As the model size is huge for railways in practice, we also propose a two-step approach to solve the model efficiently. The performance of the two-step approach is verified based on practical and virtual instances